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ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

Image Denoising Techniques Preserving Edges 

Dr N Radhika 1 , Tinu Antony 2 
1 AMRITA Vishwa Vidyapeetham, Coimbatore, India 

2 AMRITA Vishwa Vidyapeetham, Coimbatore, India 

ktinuantony @ gmail .com 

Abstract — The objective of this work is to propose an image 
denoising technique and compare it with image denoising 
using ridgelets. The proposed method uses slantlet transform 
instead of wavelets in ridgelet transform. Experimental result 
shows that the proposed method is more effective than ridgelets 
in noise removal. The proposed method is effective in 
compressing images while preserving edges. 

Index Terms — ridgelet, slantlet transform, image denoising, 
compression, huffman, edge 

I. Introduction 

Image denoising is an important step in preprocessing of 
images. It is extremely difficult to form a global denoising 
scheme effective for different types of noisy images. Wavelets 
and ridgelets exploit redundancy in the image. Thresholding 
is applied to remove the noise without blurring edges. The 
important characteristic of the denoising technique 
introduced in this paper is that it can reduce noise without 
destroying edges in an image. So edge information is 
preserved and noise is well attenuated. The paper introduces 
a technique for image denoising that replaces wavelet 
transform in ridgelets by slantlet transform. The paper also 
focuses on image compression using the proposed method. 
Sparse representation of image data is achieved via invertible 
and non-redundant transforms [1], [2]. For practical 
applications, a discrete version of ridgelet transform is used. 
The building block of finite ridgelet transform (FRIT) is finite 
radon transform. Finite radon coefficients are optimally 
ordered [6] and one dimensional wavelet is applied on each 
slice of radon coefficients to give finite ridgelet transform [7] . 
Ridgelets give better edge representations than wavelets. To 
preserve more edges with reduced number of computations, 
slantlet transform is used instead of one dimensional wavelets 
in ridgelet transform [9], [10], [11]. In this paper, the 
compression of images is also carried out with the proposed 
method. Threshold is applied to the number of transform 
coefficients taken and huffman coding is done over it. At the 
decoder module, the original image is reconstructed. Similarly 
the image compression using ridgelets is carried out [4] . Both 
the reconstructed images are compared with the help of image 
quality metrics like PSNR, RMSE, Average Difference and 
Maximum Difference [7]. The proposed method is inspired 
on a wavelet based transform: ridgelet transform which is 
reviewed later. The rest of the paper is organized as follows. 
Section II and Section III briefs ridgelet transform and slantlet 
transform respectively. Section IV explains the proposed work. 
Section V and Section VI describes how the proposed work 
can be employed for image denoising and image compression. 
Numerical results are tabulated towards the end of the paper. 

©2011 ACEEE 

II. Ridgelet Transform 

Given an integrable bivariate function f(x), its continuous 
ridgelet transform (CRT) in R 2 is defined as [4], [8] 

CST f (a,Kff)= | y^ b6 {x)f{x)dx (1) 

a 2 

where the ridgelets W a ^ q W in 2D are defined from a 
wavelet-type function in 1-D y/(x) as 

Ridgelets can be thought of as a way of concatenating ID 
wavelets along lines. In 2D points and lines are related via 
radon transform which in turn links wavelets and ridgelets. 
In the FRAT domain, energy is best compacted if the mean is 
subtracted from the image f (i, j) [3]. To reduce the wrap around 
effect of FRAT, an optimal ordering of finite radon coefficients 
is done. To these optimally ordered radon coefficients, ID 
wavelet transform is applied [8] . The ridgelets are used for 
compressing images where edge information is very critical. 
In denoising the images, ridgelets play an crucial role in 
preserving edges. 

III. Slantlet Transform 

The filterbank iteration structure of wavelet transform does 
not yield a discrete-time basis that is optimal with respect to 
time localization. Consider the equivalent structure of an 
iterated DWT filter bank. The slantlet filterbank is based on 
this structure. It will be occupied by different filters that are 
not products. With the extra degrees of freedom obtained by 
giving up the product form, it is possible to design filters of 
shorter length. The slantlet basis well suits piecewise linear 
signals, is orthogonal and it provides multiresolution 
decomposition. The filterbank is less frequency selective than 
traditional DWT filterbank due to shorter length of filters. 
The time localization is improved. Although both types of 
filterbanks, DWT and slantlet, possess same number of zero 
moments, the smoothness properties are different. The 
slantlet filter coefficients given by Selesnick [5] are 

f^_^U____. + __ru 

1W ^ 20 4 J ^ 20 4 J 

3-Jw -M -2 (-Iw V^ -3 m 

^20 4 J ^20 4 J 


ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

F 2 (z) = 

r 7-J3 3^/55 1 1 ■& ^55 \ -1 

SO + SO 

SO so 

-2 f 17^5 WsJ | -3 

2 + \--^r + -^rr 

17 V3 3^55 I -4 (9-75 -TsF 



SO ' so 

^3 -/lH -6 ' 7^5 3^55 ^ -7 

SO so 




H 2 {z) = 



z + 

1 -hi 

16 + 16 


16 J 

' 1 4n\ 

16 16 J 

: H") 


The ability to model discontinuities is relevant in applications 
like edge detection. The support of the slantlet filters are less 
than those of the filters obtained by filterbank iteration. For 
scale i, there will be a reduction of 2'-2 samples. 

IV. Proposed Method 

In ridgelets, the idea is to map a line singularity into a 
point singularity using radon transform and then wavelet 
transform can be used to effectively handle the point 
singularity in radon domain. In the proposed method, slantlet 
transform is performed on each row of radon coefficients. It 
is expected that the proposed transform will give high 
performance and strong properties. The proposed transform, 
combines together the good properties of local transforms. 
The properties of slantlet transform is higher than that of 
wavelet transform. In the FRIT domain, linear singularities 
are represented by a few large coefficients. Noisy singularities 
will be randomly located and significant coefficients are not 
generated. Hence thresholding, the FRIT coefficients can be 
very effective. The edges are critical in image analysis as 
they provide information on different regions in the image. 
By representing edges in a better way, the proposed method 
gives rich information in the spatial domain than wavelets. 
Image compression is carried out with the proposed method 
and the ridgelets. A comparative study is carried out with the 
help of different image quality metrics like RMSE (Root Mean 
Square Error), PSNR (Peak Signal to Noise Ratio), Average 
Difference and Maximum difference [7]. 

V. Image Denoising 

Assume the original image be contaminated by an additive 
Gaussian white noise of variance q-s The denoising algorithm 
consists of following steps. 

Stepl: Apply proposed method to the noisy image. 
Step2: Apply hard thresholding to the coefficients with 

universal threshold T = (7-\/21og N where N=p 2 pixels. 

Step3: Inverse of the thresholded coefficients is taken. In 
order to overcome the "wrap around" effects and to enhance 
visual appearance of restored image wiener filtering is 
employed. The following figure illustrates denoising an image 
using FRIT and the proposed method. 



Figure 1. Illustration of denoising (a) noisy image (b) using FRIT 
(c) using proposed method 

The Figure 1 .(a) is a noisy image of SNR 32.49 dB, Figure 
l.(b) employs FRIT for denoising (SNR=46.44dB) and 
denoised image using proposed method (46.50dB) is shown 
in Figure 1 .(c) SNR value is high for Figure 1 . (c) 

VI. Experimental Results 

Image compression using the proposed method and the 
ridgelet transform have been tested on many images. Here 
performance results for three images are given. 





Figure 2. Compression of different images using the FRIT and 
proposed method. 

The Figure 2. (a) to (c) show the original image (polygon.bmp), 
reconstructed image from proposed image compression and 
reconstructed image from image compression scheme using 
ridgelets respectively. Figure 2. (d) to (f) show original image 
(H shape.bmp), Figure 2. (g) to (i) show original image 
(circle.bmp) and their reconstructed images. The inferences 
obtained from the figures shown above are given in table I. 
The alphabets 'r' and 'p' denote ridgelet image compression 
and proposed image compression respectively. 

©2011 ACEEE 


ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

From the figures shown, a polygon, a H shape and a circle, it 
is evident that edges that are horizontal, vertical or having a 
slope are reconstructed better than curved edges. The 
proposed method gives better result than FRIT in the case of 
all the images shown above. 


Denoising of an image with ridgelets and proposed 
method is carried out. The proposed method provides better 
noise removal. Compression of images using two different 
techniques is also discussed. The two image compression 
techniques are image compression using proposed method 
and ridgelet. The visual quality of images and the image quality 
metrics convey that the proposed technique gives better 
results. authors can conclude on the topic discussed and 
proposed. Future enhancement can also be briefed here. 

TABLE I. Analysis using Image Quality Metrics 











Polygon [p) 





H shape(r) 





H shape[p) 











91 .54 





I wish to thank Computer Science Department of AMRITA 
Vishwa Vidyapeetham, Coimbatore for motivating me 
throughout this project. 


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©2011 ACEEE